AllAboutDecibels
The Basics
A decibel (dB) is a logarithmic comparison of two power measurements.
Let P1 and P2 be two measurements of power.
A Bel (as in Alexander Graham Bell) is defined as
B = log10 (P1 / P2)
A Bel is a huge difference, so customarily a tenth of a bel, or deciBel is used.
dB = 10 * log10 (P1 / P2)
(Decibels have never made any sense to me -- John Gilmore -- but Bels make perfect sense. So just divide by ten and think in Bels, which are just logarithms base ten. Thus 20dB is 2 Bels which is a factor of 100. Why the radio world complicated the simplicity of logs by multiplying them all by ten baffles me -- it's like calculating in furlongs per fortnight.)
dB's vis-a-vis Volts
In the electrical domain, it's sometimes more convenient to measure voltage than power.
Volts can be related to power like this: P = V*V / R, where R is a resistance. That is, power goes as the square of voltage.
For two voltages V1 and V2, measured across two resistances (impedances) R1 and R2 a little algebra gives you:
P1 = V12 / R1
P2 = V22 / R2
dB = 10 * log10 ((V12 / R1) / (V22 / R2))
If R1 == R2, this simplifies to
dB = 10 * log10 ((V1/V2)2)
db = 10 * 2 * log10 (V1/V2)
db = 20 * log10 (V1/V2)
dBm's
If you thought that was simple, they've thought of more stuff to complicate your life. A dBm is a dB value calculated against a 1-milliwatt value. Yep, not one watt, but a thousandth of a watt. Again the bogons have inserted random factors into what ought to be simple.
Thus a 5dBm signal is a 0.5 Bel signal times 0.001 watt. 0.5 Bel is 10**0.5 or about 3.16. Thus 5 dBm is an inconvenient way to write 0.00316 watts. Didn't you always want to know that?
A few handy numbers
Power
3 dB is a factor of 2 [10 * log10 (2) = 3.01]
6 dB is a factor of 4
10 dB is a factor of 10
20 dB is a factor of 100
-3 dB is a factor of 1/2
-6 dB is a factor of 1/4
-10 dB is a factor of 1/10
-20 dB is a factor of 1/100
Voltage
3 dB is a factor of 1.414
6 dB is a factor of 2
12 dB is a factor of 4
20 dB is a factor of 10
40 dB is a factor of 100
-3 dB is a factor of 0.707
-6 dB is a factor of 1/2
-12 dB is a factor of 1/4
-20 dB is a factor of 1/10
-40 dB is a factor of 1/100
